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 Ufimsk. Mat. Zh., 2015, Volume 7, Issue 3, Pages 50–56 (Mi ufa286)

Comparison Tauberian theorems and hyperbolic operators with constant coefficients

Yu. N. Drozhzhinov, B. I. Zavialov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: As comparison Tauberian theorems one usually means theorems which by a prescribed asymptotic behavior of the ratio of some integral transforms of two (generalized) functions make a conclusion on asymptotic behavior of other integral transformations of these functions. In the work we prove the comparison Tauberian function for the generalized functions whose Laplace transform have a bounded argument. In particular, examples of these functions are the kernels and the fundamental solutions of differential operators with constant coefficients hyperbolic w.r.t. a cone.

Keywords: generalized functions, Tauberian theorems, quasi-asymptotics, operators hyperbolic w.r.t. a cone.

 Funding Agency Grant Number Russian Science Foundation 14-50-00005

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English version:
Ufa Mathematical Journal, 2015, 7:3, 47–53 (PDF, 451 kB); https://doi.org/10.13108/2015-7-3-47

Bibliographic databases:

UDC: 517.53+539

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “Comparison Tauberian theorems and hyperbolic operators with constant coefficients”, Ufimsk. Mat. Zh., 7:3 (2015), 50–56; Ufa Math. J., 7:3 (2015), 47–53

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. K. Gushchin, “$L_p$-estimates for the nontangential maximal function of the solution to a second-order elliptic equation”, Sb. Math., 207:10 (2016), 1384–1409
2. Yu. N. Drozhzhinov, “Multidimensional Tauberian theorems for generalized functions”, Russian Math. Surveys, 71:6 (2016), 1081–1134
3. Yu. N. Drozhzhinov, “Asymptotically homogeneous generalized functions and some of their applications”, Proc. Steklov Inst. Math., 301 (2018), 65–81
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